{
  "abstract": "The critical Ising model admits several natural scaling limits. For an Ising model on a lattice approximation $D^a$ of a planar domain $D$, the rescaled spin field converges, as $a\\to0$, to the critical Ising magnetization field (IMF), a rough random distribution on $D$, while the spin interfaces converge to a nested $CLE_3$ and the FK--Ising representation converges to a colored $CLE_{16/3}$. In this work, we prove that the IMF can be directly reconstructed from the nested $CLE_3$. This complements the previously known construction of the IMF from the colored $CLE_{16/3}$ [CGN15]. Our result also implies that %We further show that if one constructs a colored $CLE_{16/3}$ from the nested $CLE_3$ through CLE percolation [MSW17], the resulting construction recovers the same magnetization field. A main difficulty in this present reconstruction comes from the fact that the renormalization exponent of the IMF, $15/8$, is smaller than the Hausdorff dimension of the $CLE_3$ carpet, $187/96$. Consequently, the field cannot be recovered by a direct Minkowski-content construction from the nested $CLE_3$ as is the case for $CLE_{16/3}$. We conjecture that the converse measurability also holds, namely that the nested $CLE_3$ can itself be reconstructed from the IMF.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02064",
  "author_total": 3,
  "authors": [
    {
      "name": "Paul Cahen"
    },
    {
      "name": "Christophe Garban"
    },
    {
      "name": "Avelio Sepúlveda"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cgmgejaxgz2yg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02064",
  "fulltext_url": null,
  "id": "cgmgejaxgz2yg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02064",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7215943971",
  "pdf_url": "https://arxiv.org/pdf/2610.02064",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cgmgejaxgz2yg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:03Z",
      "native_id": "2610.02064",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02064"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "The critical Ising magnetization field can be reconstructed from its $+/-$ interfaces",
  "title_text": "The critical Ising magnetization field can be reconstructed from its +/− interfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/cgmgejaxgz2yg",
  "venue": "arXiv",
  "versions": []
}